Question

Football teams $T_1$ and $T_2$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $T_1$ winning, drawing and losing a game against $T_2$ are $\frac{1}{2},\frac{1}{6}$ and $\frac{1}{3}$, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams $T_1$ and $T_2$ respectively, after two games.$P(X>Y)$ is

• A. $\frac{1}{4}$
• B. $\frac{5}{12}$
• C. $\frac{1}{2}$
• D. $\frac{7}{12}$

Answer 1

The correct option is B $\frac{5}{12}$

$P(X>Y)=WW+DW+WD$

where $W$ represents wins and $D$ represents draw

$P(X>Y)=\frac{1}{2}\cdot \frac{1}{2}+\frac{1}{6}\cdot \frac{1}{2}+\frac{1}{2}\cdot \frac{1}{6}=\frac{5}{12}$